This study proposes a new method to measure the similarity among generalized fuzzy numbers based on a standard deviation. The properties of the proposed similarity measure are demonstrated with 44 sets of generalized fuzzy numbers applied to compare the proposed method with existing similarity measures. Comparative results indicate the proposed method is better than existing methods. Solving fuzzy recommendation problems uses the proposed similarity measure.
References
[1]
Chen, S. (1998) Aggregating Fuzzy Opinions in the Group Decision-Making Environment. CyberneticsandSystems, 29, 363-376. https://doi.org/10.1080/019697298125641
[2]
Hsu, H.M. and Chen, C.T. (1996) Aggregation of Fuzzy Opinions under Group Decision Making. FuzzySetsandSystems, 79, 279-285. https://doi.org/10.1016/0165-0114(95)00185-9
[3]
Kenney, J.F. and Keeping, E.S. (1962) Linear Regression and Correlation. Mathematics of Statistics, 1, 252-285.
[4]
Chen, S. (1996) New Methods for Subjective Mental Workload Assessment and Fuzzy Risk Analysis. CyberneticsandSystems, 27, 449-472. https://doi.org/10.1080/019697296126417
[5]
Chen, S.J. and Chen, S.M. (2003) Fuzzy Risk Analysis Based on Similarity Measures of Generalized Fuzzy Numbers. IEEETransactionsonFuzzySystems, 11, 45-56. https://doi.org/10.1109/tfuzz.2002.806316
[6]
Kangari, R. and Riggs, L.S. (1989) Construction Risk Assessment by Linguistics. IEEETransactionsonEngineeringManagement, 36, 126-131. https://doi.org/10.1109/17.18829
[7]
Schmucker, K.J. (1984) Fuzzy Sets, Natural Language Computations, and Risk Analysis. Computer Science Press.
[8]
Chen, S.J. (2006) A New Similarity Measure of Generalized Fuzzy Numbers Based on Geometric-Mean Averaging Operator. 2006 IEEE International Conference on Fuzzy Systems, Vancouver, 16-21 July 2006, 1879-1886. https://doi.org/10.1109/fuzzy.2006.1681961
[9]
Chen, S. (2008) Similarity Measure between Generalized Fuzzy Numbers Using Quadratic-Mean Operator. 2008 Second International Symposium on Intelligent Information Technology Application, Shanghai, 20-22 December 2008, 440-444. https://doi.org/10.1109/iita.2008.236
[10]
Hsieh, C.H. and Chen, S.H. (1999) Similarity of Generalized Fuzzy Numbers with Graded Mean Integration Representation. Proceeding of 8th International Fuzzy Systems Association World Congress, Chinese Taipei, 17-20 August 1999, 551-555.
[11]
Lee, H.S. (1999) An Optimal Aggregation Method for Fuzzy Opinions of Group Decision. IEEE SMC’99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028), Tokyo, 12-15 October 1999, 314-319. https://doi.org/10.1109/icsmc.1999.823219
[12]
Wei, S. and Chen, S. (2009) A New Approach for Fuzzy Risk Analysis Based on Similarity Measures of Generalized Fuzzy Numbers. ExpertSystemswithApplications, 36, 589-598. https://doi.org/10.1016/j.eswa.2007.09.033
[13]
Yong, D., Wenkang, S., Feng, D. and Qi, L. (2004) A New Similarity Measure of Generalized Fuzzy Numbers and Its Application to Pattern Recognition. PatternRecognitionLetters, 25, 875-883. https://doi.org/10.1016/j.patrec.2004.01.019
[14]
Hogg, R.V. and Tanis, E.A. (2001) Probability and Statistical Inference. 6th Edition, Prentice Hall International.
[15]
Chen, S.H. (1985) Operations on Fuzzy Numbers with Function Principal. Tamkang Journal of Management Sciences, 6, 13-25. https://sid.ir/paper/590864/en
[16]
Chen, S.H. (1999) Ranking Generalized Fuzzy Number with Graded Mean Integration. Proceedings of the Eighth International Fuzzy Systems Association World Congress, 2, 899-902. https://sid.ir/paper/593576/en
[17]
Chen, S.J. and Hwang, S.L. (1922) Fuzzy Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag.
[18]
Martinez, L., Barranco, M.J., Perez, L.G. and Espinilla, M. (2008) A Knowledge Based Recommender System with Multigranular Linguistic Information. InternationalJournalofComputationalIntelligenceSystems, 1, 225-236. https://doi.org/10.2991/ijcis.2008.1.3.4
[19]
Chen, S.J. (2007) A Novel Similarity Measure for Interval-Valued Fuzzy Numbers Based on Geometric-Mean Averaging Operator. Proceedings of the BAI 2007 International Conference on Business and Information, Tokyo, 11-13 July 2007.
[20]
Choi, K., Lee, H., Kim, C. and Lee, S. (2005) The Service Quality Dimensions and Patient Satisfaction Relationships in South Korea: Comparisons across Gender, Age and Types of Service. JournalofServicesMarketing, 19, 140-149. https://doi.org/10.1108/08876040510596812
[21]
Fletcher, R.H., O’Malley, M.S., Earp, J.A., Littleton, T.A., Fletcher, S.W., Greganti, M.A., et al. (1983) Patients’ Priorities for Medical Care. MedicalCare, 21, 234-242. https://doi.org/10.1097/00005650-198302000-00010
[22]
Ware, J.E. (1977) Some Issues in the Measurement of Patient Satisfaction with Health Care Services (Vol. 6021). Rand. https://www.rand.org/pubs/papers/P6021.html
